二维单原子斐波那契类准晶电子能谱特性研究

STUDIES ON THE PROPERTIES OF ELECTRONIC ENERGY SPECTRA FOR TWO DIMENSIONAL FIBONACCI-CLASS QUASICRYSTALS WITH ONE KIND OF ATOMS

利用单电子、紧束缚、最近邻座模型 ,在重整化群的基础上 ,用分解 消元法分析了二维单原子斐波那契类准晶FC(n)的电子能谱分裂规律 ,数值计算了其电子能谱值 ,发现在一级近似下 ,该类二维准晶格中全部都只存在n×n ,n× (n + 1) ,(n + 1)× (n + 1)等三种原子簇分子 ,相应的能谱按Ym -n -l方式分裂 ,得出了其电子能谱的能级数目通式 ,发现描述其能级数目的参量存在所谓的“斐波那契类数集合” ,并且确定了该集合的前 11个整数的稳定值 ,找出了有关斐波那契类数集合的经验公式 .

In the framework of the single-electron tight-binding nearest interaction on-site model, we have studied the splitting rules of electronic energy spectra for two-dimensional Fibonacci-class quasicrystals FC(n) with one kind of atoms by means of the decomposition-decimation method based on the renormalization-group technique and have also calculated the electronic energy spectra numberically. It was found that there are only three kinds of clusters, n x n, n x (n+1) and (n+1) x (n+1) for all of the two-dimensional quasilattices FC(n) and the electronic. energy bands split as Ym-n-l. The general formula of the energy level numbers was obtained. We discovered that there was a kind of so-called Fibonacci-class-number sets for the parameters used to describe the energy level number and got the first 11 determined integers of the sets. The experienced formula have been sought out. The analytic results are confirmed by numerical simulations.